$\dfrac{d}{dx}[-5x^2-4\cos(x)]=$
Explanation: The expression to differentiate includes $\cos(x)$. Remember that the derivative of $\cos(x)$ is $-\sin(x)$. Put another way, $\dfrac{d}{dx}[\cos(x)]=-\sin(x)$. $\begin{aligned} &\phantom{=}\dfrac{d}{dx}[-5x^2-4\cos(x)] \\\\ &=-5\dfrac{d}{dx}(x^2)-4\dfrac{d}{dx}[\cos(x)] \\\\ &=-5\cdot 2x-4(-\sin(x)) \\\\ &=-10x+4\sin(x) \end{aligned}$ In conclusion, $\dfrac{d}{dx}[-5x^2-4\cos(x)]=-10x+4\sin(x)$